I don't think anyone wants to 'dribble' over the finish line, which is why it can be a sensible decision to DNF. That's surely why the professionals do it - if it becomes clear that it's not going to be your day (something you can't always be sure of beforehand) then why inflict potential damage and more exhaustion on yourself? I was told by a medic that it's the guys who insist on pushing to the finish who usually end up in need of their help.
Seren, I think it is an interesting question about which people prefer, though obviously neither is desirable. I recently had my first DNF in a half, due to illness. It was touch and go on the morning of the race but I'm glad I turned up and gave it a try. If I'd just sat at home wondering if I should have gone, that would have been worse for me. Having said that, an injury is a bit different, and if it was a 47-mile race I think I'd DNS!